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Generic curves and non-coprime Catalans

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arxiv 2210.12569 v2 pith:ECKWQIPT submitted 2022-10-22 math.AG math.CO

Eugene Gorsky , Mikhail Mazin , Alexei Oblomkov This is my paper · ORCID
classification math.AGmath.CO
keywords curvesnon-coprimecasecatalancatalanscherednikcombinatoricscompactified
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abstract

We compute the Poincar\'e polynomials of the compactified Jacobians for plane curve singularities with Puiseaux exponents $(nd,md,md+1)$, and relate them to the combinatorics of $q,t$-Catalan numbers in the non-coprime case. We also confirm a conjecture of Cherednik and Danilenko for such curves.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Instanton slices and their superpolynomials

    math.AG 2026-07 conditional novelty 7.0 of 10

    Motivic superpolynomials of plane-curve singularities are repackaged as "instanton slice" counts, conjecturally matching new DAHA superpolynomials that are claimed to produce superpolynomials for hyperbolic knots.

  2. A geometric interpretation of the Delta Conjecture

    math.CO 2024-12 conditional novelty 7.0 of 10

    The Delta Conjecture symmetric function is realized as the bigraded Frobenius character of the Borel-Moore homology of a new family of affine Springer fibers.

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